Question

The length of the second hand of a watch is $2cm$, then:

• A. the linear speed of tip of second hand is $\frac{\pi }{15}cm/s$
• B. the linear speed of the tip of second hand is uncertain
• C. the change in linear velocity vector in $15$ seconds is $\frac{\pi }{30}\sqrt{2}cm/s^2$
• D. the change in acceration vector in $15$ minutes is $\frac{{\pi }^2\sqrt{2}}{1800}cm/s^2$

Answer 1

The correct option is A the linear speed of tip of second hand is $\frac{\pi }{15}cm/s$

$V=wR$
$V=\frac{2\pi }{60}\times 2$

$V=\frac{\pi }{15}cm/s$

$V_{total}=\sqrt{V^2+V^2}=$ Change in velocity
= $V\sqrt{2}$
= $\frac{\pi }{15}\sqrt{2}$ $cm/s$.
Change in acceleration after $15$ minutes is zero
$\therefore$ The second hand will reach at the starting point